Zhizhang David Chen

The Unconditionally Stable One-Step Leapfrog ADI-FDTD Method and Its Comparisons With Other FDTD Methods

One of the major hurdles that prevent the recently developed alternating-direction-implicit finite-difference time- domain (ADT-FDTD) method from being widely used is its relatively large computational expenditures due to its sub-step computations. To address the issue, a reformulation of the unconditionally stable one-step leapfrog ADI-FDTD method and its comparisons with other FDTD methods are presented in this letter. It is found that the one-step method requires less amount of memory and CPU time than the current unconditionally stable FDTD methods and the similar memory requirement and less CPU time (when the time step is chosen to be adequately large) than the conventional FDTD method. In other words, when the unconditionally stable FDTD methods are required to solve electromagnetic problems, one is strongly recommended to use the one-step leapfrog method presented.

The Implementation of Convolutional Perfectly Matched Layer (CPML) for One-Step Leapfrog HIE-FDTD Method

The convolutional perfectly matched layer (CPML) is modified and implemented for one-step leapfrog hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method. Its stability is verified in a semi-analytical way and its effectiveness is demonstrated numerically. It is shown that even when time step size is large, the absorbing performance of CPML is still very good.

On the divergence properties of the new efficiency-improved divergence preserved ADI-FDTD method

In this paper, the new efficiency-improved divergence preserved ADI-FDTD method and its divergence property is presented. The efficiency-improved method is analytically proven to retain the expected divergence-free property while having approximately 41.7% fewer floating point operation counts in comparison with the original divergence-preserved ADI-FDTD method. Numerical example is provided to verify the theoretical proof. This work complements the theoretical foundation around the new efficiency-improved unconditionally stable ADI-FDTD method useful for modeling spatially highly resolved regions.

A subgridding scheme with the unconditionally stable explicit FDTD method

Subgriding is much desirable for FDTD modeling of small structures in large structures. However, it has remained to be very challenging for its instability. In this paper, we propose a simple subgridding scheme that takes advantage of the explicit unconditionally stable finite-difference time-domain (FDTD) method free of unstable modes: it is applied to the coarse mesh regions with larger space steps and to the fine mesh regions with small space steps. As a result, a single relatively large FDTD time step can be used in both regions and only spatial interpolation of fields at the interface between coarse mesh and subgridded fine mesh regions are needed. Numerical examples are presented to verify the effectiveness and efficiency of the proposed scheme.

One-Step Leapfrog ADI-FDTD With CPML for General Orthogonal Grids

The unconditionally stable one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is extended and developed for general orthogonal grids in this letter. It can be derived from either the conventional ADI-FDTD but with no mid-time computation, or simply conventional FDTD, just with one perturbation term added. The convolutional perfectly matched layer (CPML) is also derived for general orthogonal grids. The proposed developments are validated and further used for investigation of the earth-ionosphere cavity, with the Schumann resonant frequencies captured. It is numerically demonstrated that the proposed method is unconditionally stable and more efficient than the conventional FDTD method for the problems considered here.

One-step leapfrog ADI-FDTD method for anisotropic magnetized plasma

A one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is proposed for modelling anisotropic magnetized plasma. Two ways to derive the differential equations are presented: one from the conventional ADI-FDTD method directly and the other from the perturbation theory. The stability of the proposed method is verified numerically. In particular, its computational efficiency in modeling anisotropic magnetized plasma is shown.

A new time reversal method with extended source locating capability

Time reversal (TR) techniques have been introduced for many applications in acoustics, seismology, medical imaging, electromagnetics, and so on. One of the applications is source locating in a time-invariant environment. By performing the TR process, temporal and spatial focusing occurs at the original source location and consequently the source locations are identified. In this paper, we propose a new TR method which allows the location identifications of narrow-band sources and moving sources which have not been considered. The proposed method is built on the conventional time-reversal method and therefore retains the simplicity and robustness of the conventional TR technique. Numerical examples are given to verify the effectiveness of the proposed method.

Analysis of the late-time instability of the TDEFIE-MOT and TDMFIE-MOT methods

The late-time instability has been an issue of main concern for time-domain integral equation (TDIE) method using the march-on-time algorithms. It can be identified with by analyzing the eigenvalues of the synthetic impedance matrix of the methods. In this paper, we reformulate the TDIE methods and analyze the late-time instability of different types of TDIE. A new category of the eigenvalues is presented based on the analysis results.

Study on tunable periodic graphene split-ring resonator (GSRR) structures using FDTD method

A simple but efficient finite-difference time-domain (FDTD) method integrated with auxiliary differential equation (ADE) for modelling periodic graphene-based structures is proposed. Based on the integral form of Amperes circuital law, the derived equations are simpler than those of subcell method proposed by the others. Numerical experiments are carried out to validate our method in comparison with the results of analytical and commercial software CST. It is further applied to study some periodic graphene-based Split-Ring Resonators (GSRR) structures, and their tunable transmission properties are investigated.

A vector-based divergence-free meshless method

Unlike its conventional counterpart, a new vector basis function based meshless method that preserves the divergence property of electromagnetic fields is proposed for solving transient electromagnetic problems. Its divergence properties are investigated through numerical experiment; it is found that artificial charges generated by the proposed method are not present while they are in the conventional meshless method in source free regions.